   Chapter 1.6, Problem 10E

Chapter
Section
Textbook Problem

Determining Continuity In Exercises 1-10, determine whether the function is continuous on the entire real number line. Explain your reasoning. See Examples 1 and 2. g ( x ) = x 2 − 11 x + 30 x 2 − 25

To determine

Whether the function g(x)=x211x+30x225 is continuous on entire real number line.

Explanation

Given Information:

The provided function is g(x)=x211x+30x225.

Consider the provided function, g(x)=x211x+30x225.

The provided function is not defined when,

x225=0x2=25x=±5

The function g(x)=x211x+30x225 is a rational function. The provided function is not defined at point 5 and 5. Therefore, the domain of the function g(x)=x211x+30x225 is all real numbers except the point 5 and 5.

The term x211x+30 can be factorize as,

x211x+30=x26x5x+30=x(x6)5(x6)=(x5)(x6)

The term x225 can be factorize, use the difference of square formula a2b2=(ab)(a+b).

x225=x252=(x5)(x+5)

The provided function can be write as,

x211x+30x225=(x5)(x6)(x5)(x+5)=(x6)(x+5)

Now, choose some values for x and compute the value for g(x), in order to form the ordered pairs that will plot on the graph

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